Download 202 midterm review nonproof solutions

202 MIDTERM REVIEW NONPROOF SOLUTIONS
P.754
1-1
1)
2)
3)
4)
5)
6)
7)
8
B,O,C or D, M,J
planes AFG, ABG,GLK
DE
plane ABC and plane GHK (top and bottom planes of the figure- use any 3 noncollinear points on each plane to name them)
plane FEK
line (planes intersect in a line)
1-2
11)
n = 7, BC = 14
1-3
12)
16)
21)
194 (approx. 13.9)
(-1, 4.5)
(-28, 8)
1-5 (questions 1-5 have more than one acceptable answer, a sample is provided)
1)
2)
3)
4)
5)
6)
7)
8)
9)
BGC, FGE
BGF, CGE
BEC, CED
CEF, CED
ABE, CBE
135
8
85.5, 94.5
36.5, 53.5
1-6
1)
2)
quadrilateral, convex, regular, 90m
hexagon, concave, irregular, 156 cm
2-1
8)
False (could have different vertices)
2-2
7)
10)
A robin is a fish and an acute angle measures less than 90o
p
T
T
F
F
q
T
F
T
F
~q
F
T
F
T
p  ~q
T
T
F
T
2-3
1)
6)
7)
10)
hypothesis: no sides of a triangle are equal
conclusion: it is a scalene triangle
If a triangle has two equal sides, then it is an isosceles triangle.
If 2 lines are never intersecting, then they are parallel. (False, could be skew)
Original Conditional: If two angles are congruent angles, then they have the
same measure. T
Converse:
If two angles have the same measure, then they are
congruent.
T
Inverse:
If two angles are not congruent angles, then they do not
have the same measure. T
Contrapositive:
If two angles do not have the same measure, then they
are not congruent angles. T
PAGE 81
1)
2)
If a calculator runs, then it has batteries. If a calculator has batteries, then it
will run.
If 2 lines intersect, then they are not vertical. If two lines are not vertical, then
the lines intersect. (second statement is false)
Page 757
2-4
1)
3)
4)
If it rains, then the game will be cancelled. (by Law of Syllogism)
yes (Law of Detachment)
invalid
2-5
4)
5)
6)
7)
If 2 points lie in a plane, then the entire line containing those points lies
in that plane.
Through any two points, there is exactly one plane.
Through any three points not on the same line, there is exactly one plane.
Through any 2 points, there is exactly one line.
2-6
1)
2)
3)
Addition Property
Transitive Property
Symmetric Property
2-7
1)
2)
3)
4)
5)
6)
7)
8)
Addition Property
Symmetric Property
Transitive Property
Substitution
Reflexive Property
Subtraction Property
Addition Property
Transitive Property
2-8
2)
m11 = 60, m12 = 30, m13 = 90
3-1
1)
2)
3)
4)
5)
6)
7)
LP
planes ABM, OCN, ABC, LMN, AEP
BM , AL, EP, OP , PL, LM , MN
consecutive interior
corresponding
alternate interior
alternate exterior
3-2
1)
7)
102
2) 72
x = 10, y = 12
3-3 8) parallel
3-4 8) y = x – 3
3-5
1)
2)
3)
4)
5)
6)
7)
3) 102
4) 78
8) x = 12, y = 65
5) 108
6) 72
10) perpendicular
1
10) y   x
3
c||d If alternate exterior angles are congruent, then the lines are parallel.
None
c||d If alaternate interior angles are congruent, then the lines are parallel.
c||d If consecutive interior angles are supplementary, then the lines are parallel.
15
40
-2
3-6 1)
2)
Draw the perpendicular from P to RS .
Draw the perpendicular from J to the line containing KL .
4-2
1)
6)
60
86
4-3
1)
2)
3)
4)
ABC  FDE
JKH  JIH
RTS  UVW
LMN  NOP
4-6
1)
4)
DAB  DBA
EB  FE
2) FBG  EGB
5) BA  BC
3) BEF  BGE
6) BD  CD
4-7
5)
A(0,b) ; B(-a,0)
6) F(-b,b)
7) G(-a-2,0) ; I(0,b)
5-1
1)
4 , 27 2) 3, 37
3) 2.5, 45
5-2
1)
3)
mTPS > mTSP
mSPZ < mSZP
2) mPRZ > mZPR
4) mSPR = mSRP
5-3
1)
2)
3)
4)
ABC is not congruent to XYZ
An angle bisector of an equilateral triangle is not a median.
RS does not bisect ARC.
proof- go over in class
5-4
2)
yes
4) no
5-5
1)
XZ > OZ
2) mZIO < mZOX
4)
IO < AE
5) mAZE > mIZO
6-1
1)
84 feet
2) 60
7) 94
3) 55
8) 86
4) 120
9) 52
5) 94
10) 24
4) 4, 54
6) no
3) mAEZ = mAZE
2)
4)
7)
25.6 inches, 38.4 inches
3
45 inches, 30 inches, 25 inches
6-2
2)
yes
RSTU ~ VWXY
6-3
1)
2)
3)
4)
LNM ~ YXZ , SAS
ABC ~ TSR, AA
RTV ~ SQV , x = 3, RT = 27, SV = 30
MNL ~ PNO , x = 2.5, PN = 7.5, MN = 10.5
6-4
2
3
1)
10
2)
3)
4)
5)
x = 4, AD = 18, DR = 30, QR = 40
12
5
3.3
6-5
1)
2)
45
33